Training Diffusion Models with Noisy Data: An Exact Framework for Learning Optimal Denoisers

Core Concepts

The core message of this paper is to present the first exact framework for training diffusion models to sample from an uncorrupted distribution using only access to noisy data.

Abstract

The paper proposes a novel framework for training diffusion models using only corrupted or noisy data samples. The key technical contributions are:

A computationally efficient method for learning optimal denoisers for all levels of noise σ ≥ σn, where σn is the standard deviation of the noise in the training data. This is achieved by applying Tweedie's formula twice.

A consistency loss function for learning the optimal denoisers for noise levels σ ≤ σn. This allows the model to learn to generate samples from the uncorrupted distribution, even when only noisy data is available.

The paper also provides further evidence that foundation diffusion models, such as Stable Diffusion XL, memorize a significant portion of their training data. To mitigate this issue, the authors use their framework to fine-tune Stable Diffusion XL on corrupted data. They show that this approach reduces the amount of memorization while maintaining competitive performance.
The paper makes the following key contributions:

Presents the first exact framework for training diffusion models using only corrupted or noisy data samples.
Provides evidence that diffusion models memorize training data at a higher rate than previously known.
Demonstrates that fine-tuning diffusion models on corrupted data can reduce memorization while maintaining performance.
Open-sources the code to facilitate further research in this area.

Stats

Samples from the LAION dataset are severely corrupted by masking or adding noise, yet the Stable Diffusion XL model is able to almost perfectly reconstruct the original images.
The fraction of generated samples that have a similarity score above 0.95 (indicating near-identical to training set) is much higher when using the authors' noising method compared to the baseline method.

Quotes

"To the best of our knowledge, SDXL does not disclose its training set."
"Our method for training using corrupted samples can be used to mitigate this problem."
"We demonstrate this by fine-tuning Stable Diffusion XL to generate samples from a distribution using only noisy samples."

Key Insights Distilled From

Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data

by Giannis Dara... at arxiv.org 04-17-2024

https://arxiv.org/pdf/2404.10177.pdf

Deeper Inquiries

How can the proposed framework be extended to handle linearly corrupted data, where the available samples are of the form Y0 = AX0, for a known matrix A

To extend the proposed framework to handle linearly corrupted data, where the available samples are of the form Y0 = AX0, for a known matrix A, we can leverage the concept of Ambient Diffusion. In this scenario, the matrix A introduces a linear corruption to the data, similar to the noise levels in the original framework. By adapting the Ambient Denoising Score Matching objective and consistency loss function, we can learn optimal denoisers for different levels of corruption introduced by the matrix A. This extension would involve modifying the training process to account for the linear corruption and adjusting the sampling and denoising mechanisms accordingly. By incorporating the characteristics of linearly corrupted data into the framework, we can train diffusion models to sample from the uncorrupted distribution even in the presence of such corruption.

What are the theoretical limits of reducing memorization through training on corrupted data

Theoretical limits exist in terms of reducing memorization through training on corrupted data. While training on corrupted data can significantly mitigate the issue of training data replication, it may not completely eliminate it. The effectiveness of reducing memorization depends on various factors such as the level of corruption, the complexity of the model, and the nature of the dataset. Training on corrupted data can help in reducing memorization by introducing noise and variability into the training process, forcing the model to focus on learning essential features rather than memorizing specific training examples. However, there may still be instances where the model retains some level of memorization, especially in cases of severe corruption or highly repetitive patterns in the data. Therefore, while training on corrupted data is a powerful strategy to address memorization, it may not completely eradicate the issue in all scenarios.

Can this approach completely eliminate the issue of training data replication

The insights from this work on diffusion models can be applied to improve the robustness and privacy-preserving capabilities of other generative modeling approaches, such as Generative Adversarial Networks (GANs). By incorporating the principles of training on corrupted data and leveraging denoising mechanisms, GANs can be enhanced to reduce overfitting and memorization of training data. This approach can help GANs generate more diverse and realistic samples by focusing on learning the underlying distribution rather than replicating specific training examples. Additionally, the concept of consistency in denoising can enhance the privacy-preserving capabilities of generative models by ensuring that sensitive information in the training data is not memorized or leaked in the generated samples. By integrating these insights, generative models like GANs can achieve better generalization, robustness, and privacy protection in various applications.